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						<h1 id="firstHeading" class="firstHeading" lang="en"><span dir="auto">Field of View</span></h1>
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								<div id="siteSub">From PanoTools.org Wiki</div>
								
												
				<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><p><br />
The <b>angle of view</b> of a photograph or camera is a measure of the proportion of a scene included in the image. Simply said: How many degrees of view are included in an image. A typical fixed lens camera might have an angle of view of 50°, a <a href="Fisheye_Projection.html" title="Fisheye Projection">fisheye</a> lens can have an angle of view greater than 180° and a full <a href="Equirectangular.html" title="Equirectangular" class="mw-redirect">equirectangular</a> or <a href="Cylindrical_panorama.html" title="Cylindrical panorama">cylindrical panorama</a> would have an angle of view of 360°.
</p><p>Most people speak of <b>field of view</b> when in fact they mean <b>angle of view</b>. Field of view is the distance covered by a projection at a certain distance. So if an image exactly shows a 2 meter wide object at 1 meter distance, then the field of view is 2 meter (and the angle of view is 90°).
Angle of view is also known as <b>angle of coverage</b>.
</p>
<div class="center"><div class="floatnone"><img alt="Field-of-view.svg" src="197px-Field-of-view.svg.png" width="197" height="283" /><a class="external" href="http://wiki.panotools.org/File:Field-of-view.svg">[*]</a></div></div>
<p>From here on and on the rest of the wiki we will only speak of field of view (although we should speak of angle of view).
</p><p>Field of view is often abbreviated as <b>FoV</b>.
Usually <b>field of view</b> refers to the <b>horizontal field of view</b> (hFoV) of an image. Some applications make use of the <b>vertical field of view</b> (vFoV) which can be calculated from the <a href="Aspect_Ratio.html" title="Aspect Ratio">Aspect Ratio</a> of the image:
</p><p>For rectilinear images:
</p><p><img class="mwe-math-fallback-png-inline tex" alt="AspectRatio={\frac  {tan({\frac  {hFoV}{2}})}{tan({\frac  {vFoV}{2}})}}" src="c398d95d4b6e864a2b448a53b5a245fd.png" />
</p><p>For fisheye images (approximation):
</p><p><img class="mwe-math-fallback-png-inline tex" alt="AspectRatio={\frac  {hFoV}{vFoV}}" src="38d368a092f7d5a4d2b42bdf4d0dd89c.png" />
</p>
<h2><span class="mw-headline" id="Conversion_from_focal_length">Conversion from focal length</span></h2>
<p>The other standard measure of the <i>width</i> or <i>narrowness</i> of a lens is <a href="Focal_Length.html" title="Focal Length">Focal Length</a>.
</p><p>Assuming a <a href="Rectilinear_Projection.html" title="Rectilinear Projection">rectilinear</a> lens, the field of view can be calculated like this (<img class="mwe-math-fallback-png-inline tex" alt="size" src="f7bd60b75b29d79b660a2859395c1a24.png" /> being either width or height for the respective FoV):
</p><p><img class="mwe-math-fallback-png-inline tex" alt="FoV=2*atan\left({\frac  {size}{2*FocalLength}}\right)" src="fa5313ae442c1ac7f832c141880e3e74.png" />
</p><p>Please note that this is an approximation. The exact values depend on the location of the <a href="Entrance_pupil.html" title="Entrance pupil" class="mw-redirect">entrance pupil</a>. More information on that in <a rel="nofollow" class="external text" href="http://www.janrik.net/PanoPostings/NoParallaxPoint/TheoryOfTheNoParallaxPoint.pdf">Rik Littlefield's paper</a>.
See <a href="Fisheye_Projection.html" title="Fisheye Projection">Fisheye Projection</a> for formulas for Fisheyes<a class="external" href="http://wiki.panotools.org/Fisheyes">[*]</a>.
</p>
<h2><span class="mw-headline" id="Conversion_from_horizontal_to_vertical_and_vice_versa">Conversion from horizontal to vertical and vice versa</span></h2>
<p>For fisheye (approximation) and equirectangular images:
</p><p><img class="mwe-math-fallback-png-inline tex" alt="vFoV=hFoV*{\frac  {height}{width}}\ " src="db71893e7683801204b25f076e7db8b3.png" />
</p><p><img class="mwe-math-fallback-png-inline tex" alt="hFoV=vFoV*{\frac  {width}{height}}\ " src="89539baed8c394f4b6eea437f16b047d.png" />
</p><p>For rectilinear images:
</p><p><img class="mwe-math-fallback-png-inline tex" alt="vFoV=2*atan\left(tan\left({\frac  {hFoV}{2}}\right)*{\frac  {height}{width}}\right)" src="4d4d22d9c63b47c6f8fb7825ec5cd1db.png" />
</p><p><img class="mwe-math-fallback-png-inline tex" alt="hFoV=2*atan\left(tan\left({\frac  {vFoV}{2}}\right)*{\frac  {width}{height}}\right)" src="ab807c8735d25a66b577b029bc0e568f.png" />
</p>



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